Factor Price Equalization Theorem:

According to the factor price equalization theorem, when the prices of the output goods are equalized between countries as they move to free trade, then the prices of the factors (capital and labor) will also be equalized between countries. Free trade will equalize the wages of workers and the rents earned on capital throughout the world. The theorem assumes that the two countries share the same production technology and that markets are perfectly competitive. In a perfectly competitive market the return to a factor of production depends upon the value of its marginal productivity. The marginal productivity of a factor, like labor, in turn depends upon the amount of labor being used as well as the amount of capital. As the amount of labor rises in an industry, labor's marginal productivity falls. As the amount of capital rises, labor's marginal productivity rises. Finally the value of productivity depends upon the output price commanded by the good in the market. In autarky, the two countries face different prices for the output goods. The difference in prices alone is sufficient to cause a deviation in wages and rents between countries, because it affects the marginal productivity. However, in addition, in a variable proportions model the difference in wages and rents also affects the capital-labor ratios in each industry, which in turn affects the marginal products. All of this means that for various reasons the wage and rental rates will differ between countries in autarky. Once free trade is allowed in outputs, output prices will become equal in the two countries. Since the two countries share the same marginal productivity relationships, then only one set of wage and rental rates can satisfy these relationships for a given set of output prices. Thus free trade will equalize goods prices and wage and rental rates. Since the two countries face the same wage and rental rates they will also produce each good using the same capital-labor ratio, but different quantities of the two goods due to different quantities of factor endowments.